A new Newton-like method for solving nonlinear equations

Saheya, B.; Sui, Yunkang; Wu, Caiying

doi:10.1186/s40064-016-2909-7

Cited by 21 publications

(16 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of the methods that are based on Newton’s, Traub, Jarratt, etc. methods the order of convergence is proved (see for instance [ 8 , 9 , 10 , 11 , 12 , 13 , 14 ]), but in case of the methods that are based on metaheuristic algorithms, like the method presented in this paper, the order of convergence is not derived (see for instance [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]). This is due the fact that this order greatly varies for different values of the parameters used in the metaheuristic algorithms.…”

Section: The Algorithmmentioning

confidence: 98%

See 1 more Smart Citation

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

Gościniak

Gdawiec

2020

Entropy

View full text Add to dashboard Cite

There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton–Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm’s elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm’s operation allow to understand the influence of the proposed modifications on the algorithm’s behaviour. Understanding the impact of the proposed modification on the algorithm’s operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications.

show abstract

Section: The Algorithmmentioning

confidence: 98%

“…Despite this method is based on Newton’s method, it has slower convergence. Another method based on Newton’s method was proposed in [ 9 ]. In this method Saheya et al revised the Jacobian matrix by a rank one matrix each iteration.…”

Section: Introductionmentioning

confidence: 99%

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

Gościniak

Gdawiec

2020

Entropy

View full text Add to dashboard Cite

show abstract

“…Then convergence theorem of Newton's strategy for distinctive cases was set up by Fourier, Cauchy, and Fine. Newton initially utilized the Newton iteration to illuminate a cubic equation in 1916 [3]. Figure 1 gives a basic explanation of how the Newton's method works.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Implementation of Newton’s Algorithm Using FORTRAN

Siddiqui

Ahmad²

2020

SN COMPUT. SCI.

View full text Add to dashboard Cite

A lot of software today dealing with various domains of engineering and life sciences have to deal with non-linear problems. In order to reduce the problem to a linear problem, a lot of state of the art solutions already exist. This work focus on the implementation of Newton’s Algorithm (also known as Newton’s method), to determine the roots of a given function within a specific user defined interval. The software for this implementation is FORTRAN. Even though FORTRAN is considered to be outdated, it still has a lot of application due to its long history and the existing legacy code. The code is written in such a manner that a user can provide a function and a specific interval and the code should in turn run iterations over the interval and should display all the possible roots within that interval. The results are compared at the end for their accuracy. The program is successful in finding out all the roots within an interval.

show abstract

“…Narang et al [19] presented a fourth order two parameter Chebyshev-Halley like twopoint family for solving the nonlinear equations of large-scale systems. Saheya et al [20] presented an improved Newton method based on iterative rational approximation model. Wang and Fan [21] presented two high computational efficient derivative-free iterative methods.…”

Section: *Corresponding Authormentioning

confidence: 99%

A new iterative linearization approach for solving nonlinear equations systems

Temelcan

2020

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

View full text Add to dashboard Cite

Nonlinear equations arise frequently while modeling chemistry, physics, economy and engineering problems. In this paper, a new iterative approach for finding a solution of a nonlinear equations system (NLES) is presented by applying a linearization technique. The proposed approach is based on computational method that converts NLES into a linear equations system by using Taylor series expansion at the chosen arbitrary nonnegative initial point. Using the obtained solution of the linear equations system, a linear programming (LP) problem is constructed by considering the equations as constraints and minimizing the objective function constructed as the summation of balancing variables. At the end of the presented algorithm, the exact solution of the NLES is obtained. The performance of the proposed approach has been demonstrated by considering different numerical examples from literature.

show abstract

A new Newton-like method for solving nonlinear equations

Cited by 21 publications

References 25 publications

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

Implementation of Newton’s Algorithm Using FORTRAN

A new iterative linearization approach for solving nonlinear equations systems

Contact Info

Product

Resources

About